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Aero-acoustics and noise

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Introduction

Sound can be understood as the pressure fluctuation in a medium. Acoustics is the study of sound propagation in a medium; AeroAcoustics deals with the study of noise generated by air. Examples include the flow around the landing gear of an aircraft, or the buffeting noise caused when driving along with the window/sunroof open. As a result of the stringent conditions imposed on the Aircraft industries to limit noise pollution, focus is now shifting towards predicting the noise generated by a given aerodynamic flow. Similarly, in the automotive industry, passenger comfort is of great importance, so OEMs are keen to minimise unnecessary noise sources.

AeroAcoustics is an advanced field of fluid dynamics in which the flow scale is removed to the acoustic levels. The first advance in the field of AeroAcoustics was made by Sir James Lighthill when he presented an "Acoustic Analogy". With proper manipulation of the Euler equations, he derived a wave equation based on pressure as the fluctuating variable, and the flow variables contributing to the source of fluctuation. The resulting wave equation can then be integrated with the help of Green's Function, or can be integrated numerically. Thus, this equation can represent the sound propagation from a source in an ambient condition. With the success of the acoustic analogy, many improvements were made on the derivation of the wave equation. Two common form of the equation used in the acoustic analogy are the Ffowcs Williams - Hawkins equation and the Kirchhoff's Equation.

Although the Acoustic Analogy solves the problem of noise prediction to a great extent, focus is now shifting towards direct computation, in which noise is computed directly by the flow solver. Of course the acoustic analogy is still applied in far field propagation, but near field sound generation is resolved to a large extent. Large Eddy Simulation is widely used for these studies. DNS is still unuseable for problems of practical dimensions; industries require a code that can provide them results in a day, not a month. Hence, RANS based models (like JET3D by NASA) are widely used in industry.

One of the main difficulties in Computational AeroAcoustics is the scale of the problem. Acoustic waves have a high velocity relative to the flow structures and, at the same time, are nearly 10 orders of magnitude smaller. Also, due to the propagation to long distances, the numerical scheme should be less dissipative and less dispersive. The CFD solvers have inherent dissipation to ensure stability. This makes most robust CFD solvers incapable of simulating acoustic flows. Advanced schemes such as Dispersion Relation Preserving (DRP) schemes, compact schemes etc., aim at a less dispersive solution. Still, given the limits of current computational capability, acoustic computation for a problem of practical interest is still out of reach.

The solution adopted by the main code vendors (STAR-CD, Fluent, CFX) is to de-couple the problem: solve for the acoustic sources in the CFD code, then couple to an acoustic propagation code (SYSNoise, Actran) to discover noise levels some distance from the source.

Different Methods

DNS

Green's Function

Hydrodynamic/acoustic splitting

The hydrodynamic/acoustic splitting method (also known as viscous/acoustic splitting) has been originally proposed by Hardin and Pope (1994) for resolving the issue of scale disparity in low Mach number aeroacoustics. This method splits the direct numerical simulation (DNS) into the viscous-hydrodynamic and inviscid-acoustic calculations. The viscous flow field is computed by solving the incompressible Navier-Stokes equations, while the acoustic field is obtained by the perturbed compressible equations (PCE). This splitting method has further been modified by Shen and Sorenson (1999) and Slimon et al (1999). Recently, Seo and Moon (2005) proposed the Linearized Perturbed Compressible Equation (LPCE). The LPCE simulates the noise generation and propagation from the incompressible flow field solution in a natural way, and also could secure a consistent acoustic solution with suppressing the evolution of unstable vortical mode in the perturbed system. Since this method is based on the incompressible flow solution, it is very effective for the flows at low Mach numbers. Moreover, computational efficiency can further be enhanced, if grid system for the flow and acoustics are treated separately for resolving the scale disparity at low Mach numbers.

Higher Order Schemes for Aero-acoustics

Finite Difference

Finite Volume

Boundary Conditions

Reference

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